satisfying Write a matrix for the linear transformation T: R³ R³ ¹ () - () · () - () · ¹) - () T = T = 2 TO = 5 0 1 2 4
satisfying Write a matrix for the linear transformation T: R³ R³ ¹ () - () · () - () · ¹) - () T = T = 2 TO = 5 0 1 2 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement:**
Write a matrix for the linear transformation \(T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) satisfying:
\[
T \begin{pmatrix}
1 \\
0 \\
0
\end{pmatrix}
=
\begin{pmatrix}
2 \\
1 \\
5
\end{pmatrix}
,\quad
T \begin{pmatrix}
1 \\
1 \\
0
\end{pmatrix}
=
\begin{pmatrix}
1 \\
2 \\
1
\end{pmatrix}
,\quad
T \begin{pmatrix}
0 \\
0 \\
2
\end{pmatrix}
=
\begin{pmatrix}
0 \\
2 \\
4
\end{pmatrix}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F672bf286-8abe-4b07-9ca1-0d5b2612956c%2Fc8bbfd3c-d440-47d7-bf50-857a1f5ad7a1%2Frx9dykh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Write a matrix for the linear transformation \(T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) satisfying:
\[
T \begin{pmatrix}
1 \\
0 \\
0
\end{pmatrix}
=
\begin{pmatrix}
2 \\
1 \\
5
\end{pmatrix}
,\quad
T \begin{pmatrix}
1 \\
1 \\
0
\end{pmatrix}
=
\begin{pmatrix}
1 \\
2 \\
1
\end{pmatrix}
,\quad
T \begin{pmatrix}
0 \\
0 \\
2
\end{pmatrix}
=
\begin{pmatrix}
0 \\
2 \\
4
\end{pmatrix}.
\]
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